I continue to analyze this simulation, my immediate plan is to build an emdrive simulation with curved bottoms, taking into account the design of the antenna in the resonator. I saw many simulations of a conical resonator, but so far I decided to study curvilinear geometry using a conditional example, from a rectangular waveguide. I also analyzed antennas in different versions (dipole, frame, loop), but I do not use this experience here yet. To reduce artifacts, I performed the calculation with greater accuracy. Here is the result.
The emdrive is , by definition from SHawyer who originally did the incorrect math to make the false claim of thrust a conical frustum, other shapes are not in general relevant, and even Shawyer's bad math doesn't predict thrust.
Thank you dear meberbs, I really appreciate that you comment on the messages of all forum participants in such detail and would like to thank you for your great contribution to the discussion of Emdrive problems. Without your detailed discussions, this forum would have been completely different, much worse. Let me answer your comments.
I remember Dr. Rodal's post where he discusses
https://forum.nasaspaceflight.com/index.php?topic=40959.msg1600672#msg16006722) In great contrast to the Wright Brothers, the explanation by Shawyer goes against all fundamental knowledge of Maxwell's equations and experimental knowledge. There is nobody at a University I know of that agrees with Shawyer's explanations. Nobody at Cambridge University. Nobody at Oxford University. Nobody at MIT, Stanford, CalTech, you name it. Martin Tajmar, at TU Dresden who conducted experiments on the EM Drive under the advice of Shawyer has painstakingly divorced himself from Shawyer's explanations.
I don’t see this as a big problem, since I studied the history of the development of technology, the laws of building technical systems and according to these laws, if we discuss the concept of an ideal space engine for flying to the stars (where there are no stocks of reactive mass - propellant, where the rocket thrust is created for due to some magic), then in this engine - according to the laws of the development of technical systems - in this engine there will be such machine parts:
a) energy source
b) drive (hub, power amplifier
c) the working body - an important part that performs its main function - sets in motion the
spacecraft).
d) control system
e) transmission systemIn Emdrive there is point b) a storage device (concentrator, energy amplifier) known as a microwave resonator but there is no point c) of the working body. Therefore, Shawyer's explanations contain a problem, but his explanations are absolutely correct, since the Emdrive thrust directly depends on the quality factor of the microwave resonator. Shawyer ingeniously guessed and confirmed in his experiments that the ideal space engine needs a high-quality microwave resonator.
Note - A microwave cavity is a special case; an ideal spaceship needs a storage device, a concentrator, an energy amplifier.
Next, I quote Dr. Rhodal again
Many things in Shawyer explanation can be shown to be fundamentally wrong, foremost among this the fact that Shawyer persists, to this date, to claim that there is no radiation pressure on the conical side walls. To state, like Shawyer does that there is no radiation pressure on the conical side walls of an electromagnetically resonant truncated conical cavity goes against everything we know from Maxwell's equations. It goes against experimental facts. It goes against calculations from Finite Difference, Finite Element and Boundary Element numerical solutions (FEKO, Meep, COMSOL, etc.) all unequivocally showing that there is radiation pressure on the conical side walls. The complete opposite of the Wright Brothers, who took an experimental approach in conformity with leading knowledge at the time: incorporating the effect of viscosity, and vorticity, from a wind tunnel, to design their wings and propeller. The Wright Brothers concentrated their efforts in preventing flow separation from their wings.
I have a short answer. Shawyer only got Emdrive thrust when he invented the curved bottoms of a conical resonator. Therefore, he rightly believes that the flat side walls of the conical cavity do not help Emdrive to create rocket thrust. According to Shawyer, the side walls are not useful for fulfilling the main function of the working body of an ideal space engine. But without side walls there is no resonator - there is no technical solution for constructing a microwave resonator. The side walls of Shawyer simply interfere, this is the place where heat losses occur, where spurious effects (thermal displacements of the center of mass) occur, like artifacts of traction measurements in the laboratory and general control system settings.
Do you know what that means? That in Emdrive there is a banal technical contradiction. The side walls are needed to create conditions for the accumulation of energy (in the resonator), but the side walls interfere - since they lose energy on the Joule heating.
Bravo Emdrive, Bravo Shawyer - the technical solution to use superconductivity perfectly, successfully resolves the first technical contradiction of Emdrive. There is energy storage, but no energy loss. This is why the whole world is discussing Emdrive like this.
Realizing this, I specifically looked for a design option for the resonator, where the side walls do not harm. (remember the
space worm where the thrust (as an idea) is created at the ends?)
In this simulation of a conventional cavity, the lateral (flat walls of the waveguide) absolutely do not harm. You see it yourself on the gif in section 2. This allows you to focus on studying the curvilinear geometry of Emdrive. I will explain this in more detail below.
1. First, I will show the shape of the pulse. I tried different forms, this form is better.
This statement is meaningless because "better" is simply an undefined concept in this situation. (I could attempt a definition along the lines of "more realistic" but none of your pulses meet this particularly well.)
Here is a very simple explanation, I can show different options for the shape of the pulse. In short - they give a "bad (smeared)" EM pulse that moves along the waveguide. As a result, bad, spurious reflections appear in the curve part.
2. Then I rounded the corners of the waveguide and got a more beautiful result.
Again, arbitrary meaningless description.
I needed curvilinear geometry, and I created an example. In addition, a sharp-edged sim contains artifacts for calculating numerical simulations. Look at the diagram for calculating the integral (surface integral) radiation pressure forces on the waveguide body as a whole. We see quality smooth curves. There seems to be an incomprehensible thing in this diagram. I will explain now. This is the total force that acts on the inner surface of the waveguide from the EM field. This does not create the Emdrav rocket thrust in any way. But it seems to me (this should be discussed separately) - this diagram is very useful for monitoring, for tuning the system and should be used to create the correct settings in a laboratory experiment. (for example, I changed the pulse duration so as to be closer to the resonance frequencies of this geometry at different modes, the pulse duration strongly affects the dynamic distribution of EM fields in the curve of the waveguide, which became a microwave resonator in another sim.
Moreover, I immediately put forward an assumption, an important remark - that without this diagram it would not be possible to find the very correct Emdrive geometry, and most importantly, this is the main criterion for setting up a laboratory experiment. I can explain this in more detail.
I want to note that the radiation pressure forces are reflected using arrows on a logarithmic scale (arrow length). There is a difference of three orders of magnitude between the pressure force on the ends and the pressure forces on the straight parts. Therefore, the “arrow” on the straight part is simply not visible at this level of scale.
Since you at no point measure or quantify the momentum in the wave, it is similarly meaningless to note the magnitude of the reflection at the end. It is trivially obvious from basic physics that since the waves carry momentum in the direction of motion, an equivalent force is required to be exerted by the waveguides on the waves to revers the direction of motion. This is in no way helpful for propellantless propulsion, because the integrated force will simply balance with the force used to generate the wave to begin with (which is not part of your model.)
Fine. I quote Dr. Rodal again.
https://forum.nasaspaceflight.com/index.php?topic=39214.msg1546438#msg1546438Remember the picture?

In this equation of motion, the term m d2x/dt2 is due to the derivative with respect to time of the momentum, and hence it is analogous to the term due to the derivative with respect to time of the Poynting vector. Similarly, the spring term kx is analogous to the term due to the divergence of the stress tensor (using the stress-strain equation).
Dr. Rodal clearly points out errors. I have already shown you that I understand physics and can repeat more. See what Rodal discusses next.
The force being defined by Trunev and by Yang as just the derivative with respect to time of the Poynting vector is non-zero for a resonant cavity, for the same reason that the inertial force and the spring force are non-zero in a harmonic oscillator: it is due to the fact that energy goes from the electric field (that changes harmonically with time) to the magnetic field (that also changes harmonically with time but is out of phase) and vice-versa. In a harmonic oscillator, one has kinetic energy going into potential energy and vice-versa (with no movement of the center of mass). For steady-state oscillations, as shown by Greg Egan, Maxwell's equation's solution shows that the cyclic time average of the derivative with respect to time of the Poynting vector and the cyclic time average of the divergence of the stress tensor are both zero.
However, for the transient problem of the EM Drive (not discussed by Greg Egan in his article), both the Poynting vector field and the stress tensor fields exhibit oscillations around an exponentially decaying growth with respect to time. Thus, under transient radio-frequency excitation of a resonant cavity, the cyclic time-average of the Poynting vector field will not be zero. This does not mean that there is a net force on the center of mass that can be explained by Maxwell's equations (or by Yang-Mills equations, which also satisfy conservation of momentum). Rather, this force due to the time derivative of the Poynting vector changing exponentially with time is perfectly balanced by the force due to the divergence of the stress tensor, and vice-versa.
I don’t know how to say it right, in the end I just did
a) used a non-harmonic signal; there are no harmonic oscillators in the sim. Eventually
"the cyclic average time of the Poynting field will not be zero.
And what’s next - I don’t understand anymore, Dr. Rodal uses speech circulation
Rather, this force due to the time derivative of the Poynting vector changing exponentially with time is perfectly balanced by the force due to the divergence of the stress tensor, and vice-versa.
I can add to this a description of the old idea that the forces of electrodynamics work no faster than the speed of light, that if it is possible to realize rapid changes in the forces of radiation pressure in the curved part of the waveguide, then the zero balance will be destroyed. But this is not the most important thing, it is somehow not very interesting, it gives a small effect.
3. The next step is an analysis of the distribution of fields. We see vectors of electric and magnetic fields.
4. It is clearly seen that in the curve of a part of the waveguide over a time interval of the order of 1-3 ns, there is a very characteristic rotation of the magnetic field vectors. What is not observed in the direct part of the waveguide.
5. The Poynting vector clearly shows the movement of the energy flow, after the curve part we see the precession of the vector at small angles. In the curve part, the Poyting vector shows the "reflection path", we see multiple reflections. It seems that we directly see the trajectory of EM photons in a cavity with any geometry and we see it very well.
The actual motion of photons is a bit different, you are dealing with a non-quantum simulation, and all motion is simply the net flow of energy of countless individual photons.
I agree. But I saw bad pictures in a cavity with antennas and thought about the task of ray tracing in order to find out and adjust the correct geometry. Just a thought.
6. The calculation of eddy currents provided new visual data. It is also seen here that the vector of the electric field changes its direction sharply. It seems that in the curved part there is a magical place where the electric field "disappears" for a short time.
The term you are looking for is "interference fringe," and there are much better ways and setups to study it.
The interference is understandable, here the question is what is sharp and fast. I used the term sharply, which I understand as a term as a jerk. I saw in various scientific articles a discussion of the concept of a jerk, for example, for laboratory generation of gravitational waves or for changing the inertial mass.
Therefore, I ask a special question whether there is a jerk or a quick change in the EM field in space applications that is useful in the term. If so, Emdray should be a special working body of the machine, which creates a sharp jerk.
I also thought to add the “plus and minus” and make it so that in the crooked knee - EM impulse banallo could not create the force of radiation pressure on the curved walls. So I came up with a tricky (unipolar) impulse. Is that a good idea?
Note. In the curve part, the effect of delaying the EM pulse for a long 2 ns occurs. This can be very important.
Nothing is being delayed, in all of your simulations the timing seems completely correct for constant velocity motion of the wavefront reaching the end of the path before reflecting.
I will show what is delayed there by a separate post, with pictures.
Conclusion.
If in a curved waveguide or in an Emdrive resonator with curved bottoms, due to "new physics" (magic), non-reactive thrust of a rocket occurs,
This conclusion is simply wrong. As I have said before, it is literally logically impossible for ANY result of a simulation of existing physics to produce a result contrary to existing physics. The only options are "you messed up" and "consistent." Your simulation does NOT show anything contrary to existing physics, there is no
non-reactive thrust, you show the equivalent of a ball bouncing off of a wall and demonstrate that upon bouncing the ball exerts a force on the wall. This is not new, interesting or helpful in the context of this thread.
You did not understand my conclusion. The sim is built according to the rules of well-known physics and cannot contradict it. A completely different question was asked - WHERE there may be (in Emdrive) a place for the manifestation of physical effects from New Physics. Where does new physics live in Emdrive?
And how these effects can be useful for the purposes of space motion.
then this happens in the curved part, where there are strong deformations (swirls) of the flow of electromagnetic energy.
There aren't "swirls," there are interference effects fro the 2 waves interfering from each other.
I see the rotation of the magnetic field vector in the sim and remember the vortex magnetic field. It is there, and we should discuss this in as much detail as possible.
But to use the effects of new physics (magic) in the design of the resonator, special structural elements must be used. Call it an adapter to the new physics or a special interface. A simple copper case with a polished surface, with physics in the skin layer of micron thickness - this is clearly not enough.
Since there is literally no new physics involves, these statements are simply meaningless.
What does it mean no? This means that it must be sought, because without the new physics, Emdrive will not be able to fly to the stars, but will simply crawl like a ding drive. .

The sim clearly shows where to look and what to look for. This should be discussed more.
7. I tried to model the adapter to the new physics with the help of Brownian particles. There is a rotation of the magnetic field lines that somehow affect the so-called virtual vacuum particles.
This literally has nothing to do with anything.
This is a completely new idea, the idea that an ideal space engine needs a special working body, machine, device, adapter or interface to create special physical effects from new physics in the local operational area. This should be discussed and considered as best as possible.
Just an attempt to dream.
If you want to dream about an imaginary universe, you are in the wrong place. Pleas estop wasting your time by performing pointless simulations and then misrepresenting their results as "new physics." Failing that, please stop wasting other people's time by posting this nonsense here.
Dr. White can dream and build simulators of a stream of vacuum plasma, but Alex_O can not do this? I just wanted to show an example concept for an adapter to a new physics and conducted a training experiment in the new sim.

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Sorry for the big post.